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12
Reliable fiducial detection in natural scenes.
 Computer VisionECCV
, 2004
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An Output Sensitive Algorithm for Discrete Convex Hulls
 Comput. Geom. Theory Appl
, 1997
"... Given a convex body C in the plane, its discrete hull is C 0 = ConvexHull(C " L), where L = ZZ \Theta ZZ is the integer lattice. We present an O(jC 0 j log ffi(C))time algorithm for calculating the discrete hull of C, where jC 0 j denotes the number of vertices of C 0 , and ffi(C) i ..."
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Cited by 10 (3 self)
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Given a convex body C in the plane, its discrete hull is C 0 = ConvexHull(C " L), where L = ZZ \Theta ZZ is the integer lattice. We present an O(jC 0 j log ffi(C))time algorithm for calculating the discrete hull of C, where jC 0 j denotes the number of vertices of C 0 , and ffi(C) is the diameter of C. Actually, using known combinatorial bounds, the running time of the algorithm is O(ffi(C) 2=3 log ffi(C)). In particular, this bound applies when C is a disk. 1 Introduction Let C be a planar convex body which we assume to be sufficiently round, in the sense that the following condition holds: Let L = ZZ \Theta ZZ denote the planar integer lattice. We require that C " L is latticeconnected; that is, the union of all the horizontal and vertical unit line segments that connect between pairs of points in C " L is connected; see Figure 1. The discrete hull C 0 of C is defined as the convex hull of C " L; see figure 2 for an illustration. The discrete hull arises in sever...
L.: On three constrained versions of the digital circular arc recognition problem
 In: 15th International Conference on Discrete Geometry for Computer Imagery (DGCI09
, 2009
"... Abstract. In this paper, the problem of digital circular arcs recognition is investigated in a new way. The main contribution is a simple and lineartime algorithm for solving three subproblems: online recognition of digital circular arcs coming from the digitization of a disk having either a given ..."
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Cited by 6 (1 self)
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Abstract. In this paper, the problem of digital circular arcs recognition is investigated in a new way. The main contribution is a simple and lineartime algorithm for solving three subproblems: online recognition of digital circular arcs coming from the digitization of a disk having either a given radius, a boundary that is incident with a given point, or a center that is on a given straight line. Solving these subproblems is interesting in itself, but also for the recognition of digital circular arcs. Indeed the proposed algorithm can be iteratively used for the recognition of circular arcs. Moreover, since the algorithm is online, it provides a way for segmenting digital curves. 1
Design of Shapes for Precise Image Registration
, 1998
"... This paper deals with the problem of designing planar shapes for subpixel image registration. Basic theoretical considerations are shown to lead to a lower bound on location accuracy. Optimal registration marks achieving this bound are discussed. These optimal designs, however, require very high pri ..."
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Cited by 5 (1 self)
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This paper deals with the problem of designing planar shapes for subpixel image registration. Basic theoretical considerations are shown to lead to a lower bound on location accuracy. Optimal registration marks achieving this bound are discussed. These optimal designs, however, require very high printing or etching resolution and are inherently very sensitive to variations in the image sampling model (like scaling of grid size and rotation). More robust, optimal and suboptimal "topology preserving" registration marks are then introduced and analyzed. 1 INTRODUCTION Suppose that a planar shape is digitized by point sampling at lattice points defined by a square grid. The result is a binary twodimensional "digital image" of the shape: a pattern of zeros and ones indicating whether the corresponding grid point belongs to the shape or its background (see Figure 1). In case the planar shape is known up to an arbitrary translation in the plane, the twodimensional pattern of zeros and ones...
Digital Circles, Spheres and Hyperspheres: From Morphological Models to Analytical Characterizations and Topological Properties
, 2013
"... In this paper we provide an analytical description of various classes of digital circles, spheres and in some cases hyperspheres, defined in a morphological framework. The topological properties of these objects, especially the separation of the digital space, are discussed according to the shape of ..."
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Cited by 3 (2 self)
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In this paper we provide an analytical description of various classes of digital circles, spheres and in some cases hyperspheres, defined in a morphological framework. The topological properties of these objects, especially the separation of the digital space, are discussed according to the shape of the structuring element. The proposed framework is generic enough so that it encompasses most of the digital circle definitions that appear in the literature and extends them to dimension 3 and sometimes dimension n.
Analytical Description of Digital Circles
 16TH DISCRETE GEOMETRY FOR COMPUTER IMAGERY, NANCY: FRANCE
, 2011
"... In this paper we propose an analytical description of different kinds of digital circles that appear in the literature and especially in digital circle recognition algorithms. ..."
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In this paper we propose an analytical description of different kinds of digital circles that appear in the literature and especially in digital circle recognition algorithms.
Extension of phase correlation to subpixel registration
 IEEE Trans. on Image Processing
, 2002
"... Abstract—In this paper, we have derived analytic expressions for the phase correlation of downsampled images. We have shown that for downsampled images the signal power in the phase correlation is not concentrated in a single peak, but rather in several coherent peaks mostly adjacent to each other. ..."
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Abstract—In this paper, we have derived analytic expressions for the phase correlation of downsampled images. We have shown that for downsampled images the signal power in the phase correlation is not concentrated in a single peak, but rather in several coherent peaks mostly adjacent to each other. These coherent peaks correspond to the polyphase transform of a filtered unit impulse centered at the point of registration. The analytic results provide a closedform solution to subpixel translation estimation, and are used for detailed error analysis. Excellent results have been obtained for subpixel translation estimation of images of different nature and across different spectral bands. Index Terms—Image alignment, phase correlation, subpixel registration. I.
Online Recognition of Digital Arcs
"... This paper focuses on the online recognition of digital arcs. The main contribution is to propose a simple and linear algorithm for three subproblems: online recognition of digital arcs coming from the digitization of a disk having (i) a fixed radius, (ii) a boundary that contacts a fixed point an ..."
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This paper focuses on the online recognition of digital arcs. The main contribution is to propose a simple and linear algorithm for three subproblems: online recognition of digital arcs coming from the digitization of a disk having (i) a fixed radius, (ii) a boundary that contacts a fixed point and (iii) a center that belongs to a fixed straight line. Solving such subproblems is interesting in itself, but also for the recognition of digital arcs. Indeed the proposed algorithm can be used as an oracle in multidimensional search techniques or can be iteratively used in a naive manner. Moreover, since the algorithm is online, it is a means of segmenting digital curves in a very fast way.
VisionBased Localization using Reliable Fiducial Markers By:
, 2011
"... ~ ii ~ Visionbased positioning systems are founded primarily on a simple image processing technique of identifying various visually significant keypoints in an image and relating them to a known coordinate system in a scene. Fiducial markers are used as a means of providing the scene with a number ..."
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~ ii ~ Visionbased positioning systems are founded primarily on a simple image processing technique of identifying various visually significant keypoints in an image and relating them to a known coordinate system in a scene. Fiducial markers are used as a means of providing the scene with a number of specific keypoints, or features, such that computer vision algorithms can quickly identify them within a captured image. This thesis proposes a reliable visionbased positioning system which utilizes a unique pseudorandom fiducial marker. The marker itself offers 49 distinct feature points to be used in position estimation. Detection of the designed marker occurs after an integrated process of adaptive thresholding, kmeans clustering, color classification, and data verification. The ultimate goal behind such a system would be for indoor localization implementation in low cost autonomous mobile platforms.
DRAFT
"... This paper presents a derivation for the CramérRao Lower Bound (CRLB) of image registration error using an isotropic fiducial mark. This derived CRLB is a functional profile of the fiducial mark. Following the development of the CRLB, a new method for designing an isotropic fiducial mark, suitable ..."
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This paper presents a derivation for the CramérRao Lower Bound (CRLB) of image registration error using an isotropic fiducial mark. This derived CRLB is a functional profile of the fiducial mark. Following the development of the CRLB, a new method for designing an isotropic fiducial mark, suitable for digital image registration is presented. A parameterization method of the fiducial profile is introduced which guarantees no aliasing effect when the fiducial mark is digitized with proper sampling rate and is bandlimited. A method for computing the circular fiducial mark, based on minimization of the CRLB registration error, and subject to certain practical constrains is developed. Experimental results are used to show that the designed fiducial mark can provide very accurate registration results and that the registration accuracy is independent of its location.